calculus

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The region between the graphs of y=x^2 and y=2x is rotated around the line x=2.
The volume of the resulting solid is ____. Please help. I've tried this problem so many times but i keep getting it wrong. I thought the outer radius would be (2-0) and inner radius is (2-x^2) integrated from 0 to 2, but its not right.

  • calculus -

    They intersect at (0,0) and (2,4)

    Since you are rotationg about x = 2, we need to take horizontal slices and our
    general formula will be
    vol = pi(integral)(outer radius)^2 - (inner radius)^2 dy from 0 to 4

    Vol = pi(integral)((2-y/2)^2 - (2-√y)^2)dy from 0 to 4
    = pi[(1/12)y^3 - (3/2)y^2 + (8/3)^(3/2)] from 0 to 4

    My answer came out to be 8/3

    Let me know if your text agrees.
    =

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